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A short review on graphing inequalities. In order to graph the inequality y > 3 – x first graph the equation y = 3 – x. This line will be the borderline between the points that make y > 3 – x and the points that make y < 3 – x. In y = mx + c form we have y = -x + 3. In this case we have a line whose slope is –1 and whose yintercept is 3. 4.0 y 2.0 -4.0 -2.0 2.0 -2.0 Now we have to decide which side of the line satisfies y > 3 – x. -4.0 4.0 x A short review on graphing inequalities. All we have to do is to choose one point that is off the line and test it in the original inequality. If the point satisfies the inequality then we are on the correct side of the line and we shade that side. If the point does not satisfy the line, we shade the other side. 4.0 The most popular point to use in the shading test is (0, 0). THE TEST: substitute (0, 0) into y > 3 – x and see if you get a true statement. 2.0 -4.0 -2.0 2.0 -2.0 -4.0 0>3-0 y 0 > 3, which is false. 4.0 x Since (0, 0) did not satisfy the inequality y > 3 – x we conclude that (0, 0) is on the wrong side of the tracks and we shade the other side. Our conclusion is that every point in the shaded area is part of the solution set for y > 3 – x. 4.0 You can reinforce this idea by testing several points in the shaded area. (2, 2) 2>3–2 2>1 (0, 3) 3>3–0 3>3 (4, 1) 1>3–4 y 2.0 -4.0 1 > -1 Each point that we pick in the shaded area generates a true statement. -2.0 2.0 -2.0 -4.0 4.0 x